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As South Korean President Park Geun Hye's popularity plummets, members of her own party are publicly demanding action to staunch the bleeding from an influence-peddling scandal.

The ruling Saenuri Party wants Park to remove the prime minister and several cabinet members, and replace them with neutral appointees approved by politicians, spokesman Kim Sung Won said. It met three opposition parties to discuss the proposal, but their discussion ended in 10 minutes after disagreements, Yonhap News reported.

Prosecutors raided Park's office over the weekend to investigate allegations that her close friend Choi Soon Sil - a private citizen referred to in media as 'Rasputin's daughter' who opposition MPs have linked to a religious cult - wielded influence on state affairs over an extended period.

Park's opponents allege that Choi helped make budget and staff decisions in addition to cajoling a business lobby group to raise money for two foundations she controls.

Wearing a black hat and clothes, Choi arrived yesterday at Seoul Central District Prosecutors' Office for questioning. Surrounded by a scrum of reporters, she sobbed and appeared to nearly collapse, giving what Yonhap said was an apology to the public.

The scandal has sparked street protests throughout South Korea, serving as a crucible for a growing national frustration marked by sputtering economic growth and high-profile struggles at companies like Samsung Electronics Co. and Hanjin Shipping Co.

South Korea's financial watchdog is looking at whether KEB Hana Bank extended illicit or preferential loans to Choi and her daughter, Yonhap reported.

"If the President resigns, that could rock the markets, but long-term investors have learned a lesson that this kind of political risk doesn't really hurt the economy," Lee Chai Won, chief investment officer at Korea Investment Value Asset Management, said.

Park now faces added obstacles to passing measures that will restore confidence in the roughly 16 months she has left in office. Opposition MPs said last week they plan to more carefully scrutinise Park's 2017 Budget proposal for any sign of Choi's influence.

Park made a rare apology in a nationally televised address last week in which she said she consulted Choi on "certain documents". The President accepted the resignation of her chief of staff, part of efforts to surround herself with new advisers.

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Choi, who returned to Seoul from Germany, apologised to the public and agreed to cooperate with investigators after resting a day because she was "not in good health and also tired after a long flight," her lawyer Lee Kyung Jae told reporters in a televised briefing. He said she changed her name to Choi Seo Won.

Both the ruling and opposition parties called for her immediate arrest.

"It makes no sense that she gets one day for rest," said Youn Kwan Suk, an MP with the Opposition Democratic Party of Korea. "This is allowing her to earn time and put the puzzles together."

While the two main opposition parties have criticised Park they have not called for her resignation. If she were to step down it would trigger a presidential election in 60 days. A Gallup Korea poll in October showed the leaders of both parties trailing United Nations Secretary-General Ban Ki Moon, who hasn't confirmed either his candidacy or which party he'd join.

"Neither her resignation nor impeachment is a desirable option," Son Kum Ju, a spokesman for the second-largest opposition People's Party, said.

Economists surveyed by Bloomberg forecast South Korea to grow 2.7 per cent both this year and next. While better than most developed economies, it falls short of the country's average annual growth of 3.6 per cent over the previous decade.